Question
problems
A spring has a spring constant of 100 N/m. How much potential energy does it store when stretched by 10 cm? The spring in the Fig. has k = 140 N/m. A 50-g block is placed against the spring, this is compressed 11 cm. When the block is released, how high up the slope does it rise? Neglect friction A block of rpass 4 kg slides down a slope at a constant speed of 4 m/s. If the frictional coefficient between the slope and the block is 0.35, find the angle made by the slope with the horizontal. A 145 g baseball leaves a pitcher's hand at a speed of 32 m/s. If air drag is negligible, how much work has the pitcher done on the ball by throwing it? A 100 g baseball leaves a pitcher's hand at a speed of 30 m/s. If air drag is negligible, how much work has the pitcher done on the ball by throwing it? It takes about 30 kJ to melt an ice cube. A typical microwave oven produces 875 W of microwave power. How low long will it take a typical microwave to melt the ice cube? If the speed of a weather satellite in to its circular orbit is 7500 m/s, how high is it from the surface of the earth? [ G = 6.67 x 10 nNm2/kg2, the earth's radius = 6380 km and its mass is 5.98 x 1024 kg]
Explanation / Answer
a)energy stored = 0.5*k*x^2 = 0.5*100*0.1^2 = 0.5 J
b)energy stored = 0.5*140*0.11^2 = 0.847 J
0.847 = mgh = 0.05*9.81*h
h = 1.726 m
c) friction force = downward gravitational force
mu*mg*cos(theta) = mg*sin(theta)
tan(theta) = mu = 0.35
theta = 19.29 degrees
d)Work done = stored KE = 0.5*m*v^2 = 0.5*0.145*32^2 = 74.24 Joules
e)work done = 0.5*m*v^2 = 0.5*0.1*30^2 = 45 Joules
f) time = Energy / power = 30000/875 = 34.28 sec
g) v = sqrt(GM/r)
r = GM/v^2 = 6.67*10^-11* 5.98*10^24 / 7500^2
= 7094.14 km
heght = 7094.14 - radius of earth = 7094.14 - 6380 = 714.1 km
