(a)
The relation between the components of velocity.
(a)
Answer to Problem 48P
The relation between the components of velocity is
Explanation of Solution
Write the equation for the position of the glider.
Here,
Write the expression for the x-component of velocity.
Here,
Write the expression for the y-component of velocity.
Here,
Conclusion:
Substitute
Thus, the relation between the components of velocity is
(b)
The relation between the components of the acceleration.
(b)
Answer to Problem 48P
The relation between the components of the acceleration is
Explanation of Solution
Write the equation for the x-component of acceleration.
Here,
Write the equation for the y-component of acceleration.
Here,
Since, the glider release from rest,
Conclusion:
Substitute
Thus, the relation between the components of the acceleration is
(c)
The tension in the string.
(c)
Answer to Problem 48P
The tension in the string is
Explanation of Solution
Write the equation of motion for the counterweight.
Here,
Write the expression for the coordinate.
Here,
Write the expression for the position of glider.
Write the equation of motion for the glider by using equation (VI) and (VIII).
Conclusion:
Substitute
Thus, the tension in the string is
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Chapter 4 Solutions
Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
- A car accelerates down a hill (Fig. P4.57), going from rest to 30.0 m/s in 6.00 s. A toy inside the car hangs by a string from the cars ceiling. The ball in the figure represents the toy, of mass 0.100 kg. The acceleration is such that the string remains perpendicular to the ceiling. Determine (a) the angle and (b) the tension in the string. Figure P4.57arrow_forwardReview. A block of mass m = 2.00 kg is released from rest at h = 0.500 m above the surface of a table, at the top of a = 30.0 incline as shown in Figure P4.53. The frictionless incline is fixed on a table of height H = 2.00 m. (a) Determine the acceleration of the block as it slides down the incline. (b) What is the velocity of the block as it leaves the incline? (c) How far from the table will the block hit the floor? (d) What time interval elapses between when the block is released and when it hits the floor? (e) Does the mass of the block affect any of the above calculations? Figure P4.53 Problems 53 and 59arrow_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_forward
- At t = 0, a cart of mass m = 5 kg starts rolling down an incline, making an angle α = 20o with the horizontal. Initially the cart rolls down with no friction, but after traveling a distance of ∆ = 10 m it encounters a rough surface, where the coefficient of friction is k = 0.45. Find the acceleration of the cart along the incline (positive direction is downhill) after it encounters the rough surface. A.9.8 m/s2 B.9.2 m/s2 C.7.7 m/s2 D.3.6 m/s2 E.3.4 m/s2 F.-0.8 m/s2arrow_forwardA 1.90 kg box is moving to the right with speed 9.00 m/s on a horizontal, frictionless surface. At t = 0 a horizontal force is applied to the box. The force is directed to the left and has magnitude F(t)=( 6.00 N/s^2 )t2 If the force continues to be applied, what is the velocity of the box at 3.50 s?arrow_forwardThree F forces 1 = (2.00î + 2.00ĵ) N, F2 = (−5.00î− 3.00ĵ) N and F3 = (4.50î) N act on a body, initially at rest, producing an acceleration equal to 3 , 60m s 2 ⁄. (a) What is the direction of the acceleration vector in relation to the x-axis> 0? (b) What is the body mass? (c) What is the speed of the body after 10.0s? (d) What are the components of the velocity vector after 10.0s? Answers: (a) θ ≅ 326.3 °; (b) m = 0.500kg; (c) v = 36,0m⁄s and (d) vx = 30,0m⁄s and vy = −20,0m⁄s.arrow_forward
- A string attached to an airborne kite is maintained at an angle of 40 ° with the horizontal. If a total of 120 m of string is reeled in while bringing the kite back to the ground, what is the horizontal displacement of the kite in the process? (Assume the kite string doesn’t sag.) a.100 m b.92 m c.84 m d.77 marrow_forwardA 403.280 kg car is traveling down a 25-degree slope. At the instant that the speed is 13 m/s, the driver applied the brakes. What constant force (F), parallel to the road, must be provided by the brakes if the car is to stop in 68.310 meters? CHOICES: A. 9043.234 N B. 2908.952 N C. 8635.722 N D. 1292.535 N E. 5084.885 Narrow_forwardElena dimabato of Anolia, the princess who always cried, has an ugly block with a mass M = 8 kg that slides to the right across a rough horizontal surface with a speed of 4 m/s. There is a light rope which tugs on the block with a force T= 8 N. This is oriented above the horizon which is α = 28°. Moreover, the coefficient of kinetic friction between the surface and the ugly block is 0.312. what is the strength of tension needed for the block to stop moving at 1 meter from its initial position?arrow_forward
- A 475-gram ball is traveling horizontally at 12.0 m/s to the left when it is suddenly struck horizontally by a bat, causing it to reverse direction and initially travel at 8.50 m/s to the right. If the bat produced an average force of 1275 N on the ball, for how long (in milliseconds) was it in contact with the ball? 5.64 6.64 7.64 8.64 9.64arrow_forwardTaking a frame attached to Earth as inertial, which of the following objects cannot have inertial frames attached to them, and which are inertial reference frames?(a) A car moving at constant velocity(b) A car that is accelerating(c) An elevator in free fall(d) A space capsule orbiting Earth(e) An elevator descending uniformlyarrow_forwarda slab of mass m1 40 kg rests on a frictionless floor, and a block of mass m2 10 kg rests on top of the slab. Between block and slab, the coefficient of static friction is 0.60, and the coefficient of kinetic friction is 0.40.A horizontal force of magnitude 100 N begins to pull directly on the block, as shown. In unit-vector notation, what are the resulting accelerations of (a) the block and (b) the slab?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning