A450 kg piano is being unloaded from a truck by rolling it down a ramp at 22 degree inclined . there is negligible friction and the ramp is 11.5 m long . two workers slow the rate at which the piano moves by pushing with a combined force of 1420n parralel to the ramp . i f the piano starts fromm rest . how fast is it moving at the

To solve this problem we will apply the linear motion kinematic equations, and force related equations in Newton's second Law.

Our values are given by:

Through equilibrium we know that the Force coming from the vertical weight component minus the Force exerted on the body must be equal to the total Force (Mass and acceleration). So,

Applying the kinematic equations of motion in which the velocity is described by the change in acceleration and position we have

Therefore the Speed at the bottom is 3.44m/s

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft