: Three persons wants to push a wheel cart in the direction marked x in Fig. [04 Marks]
The two person push with horizontal forces F1 and F2 as shown in the figure.
(a) Find the magnitude and direction of the force that third person should exert to stop this cart. You can ignore the effects of friction.
(b) If the third person exerts the force found in part (a), the cart accelerates at 200 m/S2 in the (+) x-direction. What is the weight of the cart?
To find the answers to these questions, we need to analyze the forces acting on the cart.
(a) To find the magnitude and direction of the force that the third person should exert to stop the cart, we need to consider the forces acting in the horizontal direction.
In the given figure, we can see two forces acting horizontally, F1 and F2, in the positive x-direction. To stop the cart, an equal and opposite force should be applied in the negative x-direction.
To calculate the magnitude of this force, we need to find the sum of the forces F1 and F2 and then take the negative of that value.
So, the magnitude of the force the third person should exert would be:
Magnitude of force = -(|F1| + |F2|)
The direction of the force would be in the negative x-direction.
(b) Now, if the third person exerts the force found in part (a), and the cart accelerates at 200 m/s^2 in the positive x-direction, we can calculate the weight of the cart.
The force required to accelerate an object can be determined using Newton's second law:
Force = mass * acceleration
In this case, the force is the force exerted by the third person found in part (a), and the acceleration is given as 200 m/s^2.
Rearranging the equation, we have:
mass = Force / acceleration
Substituting the known values, we can find the weight of the cart.