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3 years ago

A shopper does 157 J of work pushing a cart with 10.9 N force

Physics

1 answer:

Tanzania [10]3 years ago

4 0

The cart travelled a distance of 14.4 m

Explanation:

The work done by a force when pushing an object is given by:

$W=Fd cos \theta$

where:

F is the magnitude of the force

d is the displacement

$\theta$ is the angle between the direction of the force and the displacement

In this problem we have:

W = 157 J is the work done on the cart

F = 10.9 N is the magnitude of the force

$\theta=0^{\circ}$ , assuming the force is applied parallel to the motion of the cart

Therefore we can solve for d to find the distance travelled by the cart:

$d=\frac{W}{F cos \theta}=\frac{157}{(10.9)(cos 0)}=14.4 m$

Learn more about work:

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Explanation:

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moment of inertia, I, of a hollow cylinder = ¹/₂mr²

substitute for I in the equation above;

$\frac{1}{2}mv_i^2 + \frac{1}{2} (\frac{1}{2}mr^2 \omega_i^2) = \frac{1}{2}mv_f^2 + \frac{1}{2} (\frac{1}{2}mr^2 \omega_f^2) + mgh\\\\ but \ v = r \omega\\\\\frac{1}{2}mv_i^2 + \frac{1}{2} (\frac{1}{2}m v_i^2 ) = \frac{1}{2}mv_f^2 + \frac{1}{2} (\frac{1}{2}m v_f^2) + mgh\\\\\frac{1}{2}mv_i^2 +\frac{1}{4}mv_i^2 = \frac{1}{2}mv_f^2 +\frac{1}{4}mv_f^2 +mgh\\\\\frac{3}{4}mv_i^2 = \frac{3}{4}mv_f^2 +mgh\\\\mgh = \frac{3}{4}mv_i^2 - \frac{3}{4}mv_f^2\\\\gh = \frac{3}{4}v_i^2 - \frac{3}{4}v_f^2\\\\$

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given;

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