(a)
The time interval in which the smaller block make it to the right side of the
(a)
Answer to Problem 55P
The time interval in which the smaller block make it to the right side of the
Explanation of Solution
The free body diagram of the top block is shown in Figure 1.
The free diagram of the bottom block is shown in Figure 2.
From the Figure 1, write the expression for net force in the
Here,
Apply Newton’s law in the
Here,
Equate the equation (I) and (II).
From the Figure 2, write the expression for net force in the
Apply Newton’s law in the
Here,
Equate the equation (IV) and (V).
Write the expression for frictional force.
Use equation (VII) in (III).
Use equation (VII) in (VI).
Consider the Figure 3.
In the time
The necessary condition to reach the top block at the right edge of the bottom block is,
Here,
Use
Conclusion:
Substitute,
Substitute,
Substitute,
Therefore, the time interval in which the smaller block make it to the right side of the
(b)
The distance in which the
(b)
Answer to Problem 55P
The distance in which the
Explanation of Solution
Conclusion:
Substitute,
Therefore, the distance in which the
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Chapter 5 Solutions
Principles of Physics: A Calculus-Based Text
- In Figure P4.53, the incline has mass M and is fastened to the stationary horizontal tabletop. The block of mass m is placed near the bottom of the incline and is released with a quick push that sets it sliding upward. The block stops near the top of the incline as shown in the figure and then slides down again, always without friction. Find the force that the tabletop exerts on the incline throughout this motion in terms of m, M, g, and .arrow_forwardA block of mass m = 2.00 kg rests on the left edge of a block of mass M = 8.00 kg. The coefficient of kinetic friction between the two blocks is 0.300, and the surface on which the 8.00-kg block rests is frictionless. A constant horizontal force of magnitude F = 10.0 N is applied to the 2.00-kg block, setting it in motion as shown in Figure P5.103a. If the distance L that the leading edge of the smaller block, travels on the larger block is 3.00 m. (a) in what lime interval will the smaller block make it to the right side of the 8.00-kg block as shown in Figure P5.103b? (Note: Both blocks are set into motion when F is applied.) (b) How far does the 8.00-kg block move in the process?arrow_forwardFIGURE P5.49 Problems 49 and 50. Suppose the system of blocks in Problem 49 is initially held motionless and, when released, begins to accelerate. a. If m1 = 7.00 kg, m2 = 2.00 kg, and the magnitude of the acceleration of the blocks is 0.134 m /s2, find the magnitude of the kinetic frictional force between the second block and the ledge. b. What is the value of the coefficient of kinetic friction between the block and the ledge?arrow_forward
- Consider the three connected objects shown in Figure P5.43. Assume first that the inclined plane is frictionless and that the system is in equilibrium. In terms of m, g, and , find (a) the mass M and (b) the tensions T1 and T2. Now assume that the value of M is double the value found in part (a). Find (c) the acceleration of each object and (d) the tensions T1 and T2. Next, assume that the coefficient of static friction between m and 2m and the inclined plane is s and that the system is in equilibrium. Find (e) the maximum value of M and (f) the minimum value of M. (g) Compare the values of T2 when M has its minimum and maximum values. Figure P5.43arrow_forwardA 9.00-kg hanging object is connected by a light, inextensible cord over a light, frictionless pulley to a 5.00-kg block that is sliding on a flat table (Fig. P5.7). Taking the coefficient of kinetic friction as 0.200, find the tension in the string. Figure P5.7arrow_forwardWhy is the following situation impossible? A 1.30-kg toaster is not plugged in. The coefficient of static friction between the toaster and a horizontal countertop is 0.350. To make the toaster start moving, you carelessly pull on its electric cord. Unfortunately, the cord has become frayed from your previous similar actions and will break if the tension in the cord exceeds 4.00 N. By pulling on the cord at a particular angle, you successfully start the toaster moving without breaking the cord.arrow_forward
- A box with mass m1 = 6.00 kg sliding on a rough table with a coefficient of kinetic friction of 0.220 is connected by a mass-less cord strung over a mass-less, frictionless pulley to a second box of mass m2 = 12.0 kg hanging from the side of the table (Fig. P5.51). What is the tension in the cord connecting the boxes?arrow_forwardIn Example 4.5, we pushed on two blocks on a table. Suppose three blocks are in contact with one another on a frictionless, horizontal surface as shown in Figure P4.49. A horizontal force F is applied to m1. Take m1 = 2.00 kg, m2 = 3.00 kg, m3 = 4.00 kg, and F = 18.0 N. (a) Draw a separate free-body diagram for each block. (b) Determine the acceleration of the blocks. (c) Find the resultant force on each block. (d) Find the magnitudes of the contact forces between the blocks. (e) You are working on a construction project. A coworker is nailing up plasterboard on one side of a light partition, and you are on the opposite side, providing backing by leaning against the wall with your back pushing on it. Every hammer blow makes your back sting. The supervisor helps you put a heavy block of wood between the wall and your back. Using the situation analyzed in parts (a) through (d) as a model, explain how this change works to make your job more comfortable. Figure P4.49arrow_forwardInitially, the system of objects shown in Figure P5.49 is held motionless. The pulley and all surfaces and wheels are frictionless. Let the force F be zero and assume that m1 can move only vertically. At the instant after the system of objects is released, Find (a) the tension T in the string, (b) the acceleration of m2, (c) the acceleration of M, and (d) the acceleration of m1. (Note: The pulley accelerates along with the cart.) Figure P5.49 Problems 49 and 53arrow_forward
- A block of mass m = 5.8 kg is pulled up a = 25 incline as in Figure P4.24 with a force of magnitude F = 32 N. (a) Find the acceleration of the bloc k if the incline is frictionless. (b) Find the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.10. Figure P4.24arrow_forwardTwo blocks of mass 3.50 kg and 8.00 kg are connected by a massless string that passes over a frictionless pulley (Fig. P4.47). The inclines are frictionless. Find (a) the magnitude of the acceleration of each block and (b) the tension in the string. Figure P4.47arrow_forwardThree crates with masses m1 = 5.45 kg, m2 = 7.88 kg, and m3 = 4.89 kg are in contact on a frictionless surface. A horizontal force F = 205 N is applied to the third crate as shown in Figure P5.83. a. What is the magnitude of the contact force between crates 1 and 2? b. What is the magnitude of the contact force between crates 2 and 3? FIGURE P5.83arrow_forward
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