Question

A grocery cart with a mass of 16 kg is pushed at constant speed along an aisle by a force fp = 12 n which acts at an angle of 17° below the horizontal. find the work done by each of the forces on the cart if the aisle is 13 m long. work done by the applied force

Answer 1

Solution for this problem is we will be using the following formula:

Work done by applied force) = Force (applied) x s x cos θ

Where:

Force applied = 12 N

s = 13 m long

Angle = 17

So plugging in the values:

=>W (a) = 12 x 13 x cos 17

= 12 x 12.43196182

= 149.1835 J 

Answer 2

Work done by the applied force : Wp = 149,184 J

Further explanation

Work is the transfer of energy caused by the force acting on a moving object

Work is the product of force with the displacement of objects.

Can be formulated

W = F x S

W = Work, J, Nm

F = Force, N

S = distance, m

Force and displacement of objects are vector . Multiplication of both is in accordance with the dot product concept of two vectors. Whereas W is a scalar quantity. Then if there is an angle formed by the force F and the displacement S is θ, then it can be formulated

W = F cos θ.S

There are 4 forces on the cart , so there are 4 work that occurs

• work done by the applied force = Wp

= Fp.cos θ. S

= 12. cos 17. 13

Wp = 149,184 J

 

• work done by the frictional force = Wf

the magnitude is the same as the force applied by the applied force (Fp) but the opposite direction = -149,184 J

•  work done by the normal force = Wn

the direction is upward with an angle of θ = 90°, with F = mg

Wn = Fn.cos 90. S

Wn = mg cos 90. 13

Wn = 0

work done by the gravitational force = Wg

Wg = Fg. cos 90. S.

Wg = mg cos 90. 13

Wg = 0

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