Why is the following situation impossible? In a new casino, a supersized pinball machine is introduced. Casino advertising boasts that a professional basketball player can lie on top of the machine and his head and feet will not hang off the edge! The hall launcher in the machine sends metal halls up one side of the machine and then into play. The spring in the launcher (Fig. P7.44) has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined θ = 10.0° with respect to the horizontal. The spring is initially compressed its maximum distance d = 5.00 cm. A ball of mass 100 g is projected into play by releasing the plunger. Casino visitors find the play of the giant machine quite exciting.
Figure P7.44
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Chapter 7 Solutions
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- A block is placed on top of a vertical spring, and the spring compresses. Figure P8.24 depicts a moment in time when the spring is compressed by an amount h. a. To calculate the change in the gravitational and elastic potential energies, what must be included in the system? b. Find an expression for the change in the systems potential energy in terms of the parameters shown in Figure P8.24. c. If m = 0.865 kg and k = 125 N/m, find the change in the systems potential energy when the blocks displacement is h = 0.0650 m, relative to its initial position. FIGURE P8.24arrow_forwardA 6 000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in Figure P6.27 (page 188). Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2, = 3 400 N/m. After the first spring compresses a distance of 30.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 50.0 cm after first contacting the two-spring system. Find the cars initial speed.arrow_forward7.43 A block with mass 0.50 kg is forced against a horizontal spring of negligible mass, compressing the spring a distance of 0.20 m (Fig. P7.43). When released, the block moves on a horizon- tal tabletop for 1.00 m before coming to rest. The spring constant k is 100 N/m. What is the coefficient of kinetic friction between Hk the block and the tabletop? Figure P7.43 k = 100 N/m +0.20 m 1.00 m m = 0.50 kgarrow_forward
- A 1.30 kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P7.54). The object has a speed of vi = 2.60 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. The object finally comes to rest a distance D to the left of the unstretched spring. Figure P7.54 (a) Find the distance of compression d. m(b) Find the speed v at the unstretched position when the object is moving to the left. m/s(c) Find the distance D where the object comes to rest. marrow_forward12.Superman wanted to launch a small rocket using a spring mounted vertically on the ground. He placed the 4.0 kg rocket on a very stiff spring. The spring is 1.5m long, it has negligible mass and a spring force constant of 100,000 N/m. He compresses the spring for 1.1m. He then releases the spring. If y = 0 at the ground level, the system consists of the rocket and the spring; (I) what is the energy of the system before Superman releases the rocket? (II)What is the maximum height the rocket can reach if we can neglect air resistance? (III) If air resistance can't be neglected, it exerts a constant force of 37.5N on the rocket, how high will the rocket reach? (IV) What is the speed of the rocket when it is 120.0 m from the ground if air resistance is taken into account?arrow_forward2. Maria and Rory are using a spring launcher to move a 125 g block to the top of a ramp. The spring launcher is at the base of the ramp and consists of a platform and a spring with a force constant of 420 N/m. The horizontal surface at the base of the ramp is smooth and frictionless. They compress the spring by 0.12 m with the block resting against the spring launcher. Once they let go, the block travels up the 1.4 m ramp and comes to rest at the top of the ramp. The top of the ramp is 1.0 m above the ground. Ramp Experiment Ad= 1.4 m smooth frictionless surface What is the average frictional force acting on the block as it moves up the ramp? Ah=1.0 marrow_forward
- A block of mass m 2.00 kg slides along a horizontal table with speed vo 9.50 m/s. At x = 0 it hits a spring with spring constant k95.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by u 0.100. How far has the spring compressed by the time the block first momentarily comes to rest? wwwww.wl Number 9.50 m/s m Ar ?arrow_forwardHello can you solve the last 3 parts? Thank you!arrow_forwardA 18.0 g bullet is fired horizontally into a 109 g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 122 N/m. The bullet becomes embedded in the block and then compresses a spring. (a) Determine the potential energy of the spring when it is compressed by 1.00 m. A 18.0 g bullet is fired horizontally into a 109 g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 122 N/m. The bullet becomes embedded in the block. The bullet block system compresses the spring by a maximum of 1.00 m. (b) Determine the velocity of the block once the bullet is embedded, just before it starts to compress the spring. A 18.0 g bullet is fired horizontally into a 109 g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 122 N/m. The bullet becomes embedded in the block. The bullet block…arrow_forward
- In a needle biopsy, a narrow strip of tissue is extracted from a patient with a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be fired into the patient's body by a spring. Assume the needle has mass 5.60 g, the light spring has force constant 440 N/m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. (The spring is fully uncompressed before the needle contacts the skin.) The tip of the needle then moves through 2.40 cm of skin and soft tissue, which exerts a resistive force of 7.50 N on it. Next, the needle cuts 3.50 cm into an organ, which exerts a backward force of 9.70 N on it. (a) Find the maximum speed of the needle. m/s(b) Find the speed at which a flange on the back end of the needle runs into a stop, set to limit the penetration to 5.90 cm. m/sarrow_forwardA 6 000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in Figure P7.59. Both springs are described by Hooke’s law and have spring constants k1 = 1 600 N/m and k2 — 3 400 N/m. After the first spring compresses a distance of 30.0 cm. the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 50.0 cm after first contacting the two-spring system. Find the car’s initialspeed.arrow_forwardIn a needle biopsy, a narrow strip of tissue is extracted from a patient with a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be fired into the patient's body by a spring. Assume the needle has mass 5.60 g, the light spring has force constant 395 N/m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. (The spring is fully uncompressed before the needle contacts the skin.) The tip of the needle then moves through 2.40 cm of skin and soft tissue, which exerts a resistive force of 7.10 N on it. Next, the needle cuts 3.50 cm into an organ, which exerts a backward force of 9.40 N on it. (a) Find the maximum speed of the needle. m/s (b) Find the speed at which a flange on the back end of the needle runs into a stop, set to limit the penetration to 5.90 cm. m/sarrow_forward
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