A pendulum of length L with a bob of mass m swings back and forth. At the low point of its motion (point Q), the tension in the string is (3/2)mg. What is the speed of the bob at this point? A. 2gL B. 2gL C. Vgl P R gL VD. 2 VgL Е. 2
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- Two blocks are connected by a light string that passes over a frictionless pulley as in Figure P5.38. The system is released from rest while m2 is on the floor and m1 is a distance h above the floor. (a) Assuming m1 m2, Find an expression for the speed of m1 just as it reaches the floor. (b) Taking m1 = 6.5 kg, m2 = 4.2 kg, and h = 3.2 m, evaluate your answer to part (a), and (c) find the speed of each block when m1 has fallen a distance of 1.6 m. Figure P5.38A vertical massless spring with spring constant of 740 N/m, is attached to a table and is compressed down by 0.200 m. (a) what upward speed can it give to a 500 g ball when released? (b) How high above its original position (spring uncompressed) will the ball fly?Two blocks are connected by a light string that passesover a frictionless pulley as in Figure P5.38. The system is released from rest while m 2 is on thefloor and m1 is a distance h above thefloor. (a) Assuming m 1 >m 2, find anexpression for the speed of m1 justas it reaches the floor. (b) Takingm 1 = 6.5 kg, m 2 = 4.2 kg, andh = 3.2 m, evaluate your answer topart (a), and (c) find the speed ofeach block when m 1 has fallen a distanceof 1.6 m.
- Tarzan grabs a vine hanging vertically from a tall tree when he is running at 9.0 m/s. (a) How high can he swing upward? (b) Does the length of the vine affect this height?The thrust created by a lone jet engine produces a force of F = 78000 N. It takes the aircraft (with a mass of m = 7300 kg) a distance of d = 0.71 km to take off. a.) What is the take-off speed of the aircraft vt in m/s? b.) How far in meters would you need to depress a giant spring k = 100,000 N/m in order to launch the aircraft at the same speed without help from the engine?a pendulum of length L= 1.25 m. Its bob (which effectively has all the mass) has speed v0 when the cord makes an angle u0 =40.0 with the vertical. (a) What is the speed of the bob when it is in its lowest position if v0 = 8.00 m/s? What is the least value that v0 can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c) to a vertical position with the cord remaining straight? (d) Do the answers to (b) and (c) increase, decrease, or remain the same if u0 is increased by a few degrees?
- A 0.505-kg block slides on a frictionless horizontal surface with a speed of 1.18 m>s. The block encounters an unstretched spring and compresses it 23.2 cm before coming to rest. (a)What is the force constant of this spring? (b) For what length of timeis the block in contact with the spring before it comes to rest? (c) Ifthe force constant of the spring is increased, does the time required tostop the block increase, decrease, or stay the same? Explain.Tarzan grabs a vine hanging vertically from a tall tree when he is running at 9.0m/s.. (a) How high can he swing upward? (b) Does the length of the vine affect this height?A 3.00 kg fish is attached to the lower end of a vertical spring that has negligible mass and force constant 900 N/m. The spring initially is neither stretched nor compressed. The fish is released from rest. (a) What is its speed after it has descended 0.0500 m from its initial position? (b) What is the maximum speed of the fish as it descends?
- 3. To the finite! A block with mass ? = 1.20 [kg] at rest is pressed against a spring with spring constant ? = 255 [N/m], compressing it by 18.0 [cm]. The mass is then let go, and goes up a ramp inclined at an angle ? = 35.0 ◦ above the horizontal. A. What is the speed of the block immediately before it goes up the incline?B. How far along the incline’s length does the block travel until it comes to a rest?A 500000 g roller coaster car traveling at 30 m/s is stopped by a spring with a spring constant of 60,000 N/m. By how much does the spring compress in stopping the car?You fire a bullet into a 2 kg wooden block that is hanging at the bottom of a pendulum. When the bullet strikes the block, the pendulum swings upward. The bullet has a mass of 0.02 kg and strikes the block with a speed of 300 m/s. a. What is the speed of the block and bullet when they first start moving together? b. What is the maximum height reached by the pendulum?