A box of mass 5.0 kg is accelerated from rest by a force a cross a floor at a ra

Question

A box of mass 5.0 kg is accelerated from rest by a force a cross a floor at a rate of 3.0 m/s^2 for 8.0 s. Find the net work done on the box. An atomic nucleus initially moving at 400 m/s emits an alpha particle in the direction of its initial velocity, and the remaining nucleus slows to 280 m/s. If the alpha particle has mass of 4 u and the original nucleus has mass of 200 u, what speed does the alpha particle have when it is emitted? A 0.145 kg baseball pitched horizontally at 27.0 m/s strikes a bat and pops straight up to a height of 31.5 m. If the contact time between bat and ball is 2.5 ms. Calculate the average force between the ball and bat during the contact. Express the following angle in radians (give a numerical values and as a fractions of pi) (a) 45.0 degree, (b) 60.0 degree, (c) 90.0 degree. What is the angular momentum of a 0.30 kg ball revolving on the end of a thin string in a circle of radius 1.35 m at an angular speed of 10.0 rad/s? (a) a grinding wheel 0.35 m in diameter rotates at 2200rpm. Calculate its angular velocity in rad/s. (b) what are the linear speed and acceleration of a point on the edge of the grinding wheel?

Explanation / Answer

1) acceleration = (change in velocity) / time
Vi = velocity initial
Vf = velocity final

acceleration = (Vf - Vi) / time
3.0m/s² = (Vf - 0m/s) / 8.0s)
24.0m/s = Vf

(average velocity) = distance / time
(Vi + Vf) / 2 = distance / time
(0m/s + 24.0m/s) / 2 = distance / 8.0s

distance = 96m
so it is pushed 96 meters over the 8 seconds.

Now, the force on the object is given by:
F = m*a
F = 5.0kg * 3.0m/s²
F = 15 N

Work is:
W = F*d
W = 15N * 96m
W = 1440 Joules

2)  Before the emission of an alpha particle:
momentum of the original nucleus: 200×400
total momentum: M1 = 200×400
After the emission
momentum of the remaining nucleus: 196×280
momentum of the alpha particle: 4v
total momentum: M2 = 196×280 + 4v
By the law of conservation of momentum:
M2 = M1
196×280 + 4v = 200×400
4v = 200×400 – 196×280
v = 6280 m/s

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