Question

a 450 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 bottom???

Answer 1

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:

$m = 450 kg$

$x = 11.5m$

$F = 1420 N$

$\theta = 22\°$

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,

$\sum F = ma \\F_w sin(22) - F = ma\\(mg)sin(22) - F = ma\\(450)(9.8)sin(22) - 1420 = 450a\\a = 0.515 m/s^2$

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

$v_f^2 = v_i^2 + 2ax$

$v_f^2 = 0 + 2(0.515)(11.5)$

$v_f = 3.44 m/s$

Therefore the Speed at the bottom is 3.44m/s

Answer 2

The velocity of the piano is the change in its position with the given time interval. The velocity of the piano is 3.42 m/s.

What is velocity?

The velocity is the rate at which the position of the object changes.

Given that the mass m of the piano is 450 kg and its length l is 11.5 m. The angle of inclination $\theta$ is 22 degrees and the force F parallel to the ramp is 1420 N.

The total force of the system is given as below.

$F' = F sin 22^\circ - F$

$ma = mg sin 22^\circ - 1420$

$450 \times a = 450 \times 9.8 \times 0.374 - 1420$

$a = 0.51 \;\rm m/s^2$

If the initial velocity of the piano is 0 then its final velocity is given as below.

$v^2 = u^2 + 2al$

$v^2 = 0 + 2 \times 0.51 \times 11.5$

$v = \sqrt{11.73}$

$v = 3.42 \;\rm m/s$

Hence we can conclude that the velocity of the piano is 3.42 m/s.

To know more about the velocity, follow the link given below.

https://brainly.com/question/862972.