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# sample exam questions (please do in word): A block of mass 2.5 kg is placed against a compressed spring (k = 2900 N/m) at the bottom of an inclined plane, as shown

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6. A block of mass 2.5 kg is placed against a compressed spring (k = 2900 N/m) at the bottom of an inclined plane, as shown. When the spring is released the block is projected up the incline and the spring expands by 14 cm to its normal length.
Calculate the maximum distance traveled by the block up the incline without friction.
Repeat the calculation with friction, taking µk = 0.22.

7. A 15,000 kg loader traveling east at 20 km/h turns south and travels at 25 km/h. Calculate the change in the loader's
kinetic energy.
linear momentum.

8. A 470-g firework is traveling straight up at 13 m/s when it explodes into two pieces. The smaller piece (150 g) shoots off horizontally towards the East at 20 m/s. Find the speed and direction of the other piece directly after the explosion.

9. Three masses are positioned on a frictionless surface, as shown. Initially, mass m1 (1.0 kg) moves with a velocity of 2.0 m/s to the right, mass m2 (2.0 kg) is at rest, and mass m3 (3.0 kg) moves to the left with a velocity of 0.50 m/s. First, mass m1 collides elastically with mass m2 and recoils to the left. Afterwards, mass m3 collides with mass m2 and sticks. Calculate,
a)the speeds of masses m1 and m2 after the first collision.
b)the speeds of masses m2 and m3 after the second collision.

10. A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown. If the first ball moves away with angle 30° to the original path, determine
a)the speed of the first ball after the collision.
b)the speed and direction of the second ball after the collision.

##### Solution Summary

A block of mass 2.5 kg is placed against a compressed spring is examined.

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6. A block of mass 2.5 kg is placed against a compressed spring (k = 2900 N/m) at the bottom of an inclined plane, as shown. When the spring is released the block is projected up the incline and the spring expands by 14 cm to its normal length.
Calculate the maximum distance traveled by the block up the incline without friction.
Repeat the calculation with friction, taking µk = 0.22.

Without friction
The distance traveled will be maximum when the block comes to rest again at the top. For this the velocity and hence the kinetic energy of the block will be zero. As there is no friction, whole elastic potential energy initially stored in the compressed spring is utilized in doing work against gravity i.e. converts in gravitational potential energy. Hence according to law of conservation of energy we can write
Gain in gravitational potential energy = loss in elastic potential energy
Now say the maximum distance covered be l, initial compression in the spring be  l (= 0.14 m) and the angle of inclination be  (=250).

Gain in vertical height will be h= l sin . Thus

Or
Or
Gives
With friction
If the coefficient of kinetic friction is k, whole elastic potential energy initially stored in the compressed spring is utilized in doing work against friction and against gravity. Hence according to work energy rule we can write
Work done against friction = loss in elastic potential energy - Gain in gravitational potential ...

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