Threepersons wants to push a wheel cart in the direction marked x in Fig. 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?
I can not see your figure. You can not copy and paste here. Give x and y components for everything. Remember F = m A and weight = m g
To solve this problem, we will analyze the forces acting on the cart and apply Newton's second law of motion.
(a) To find the magnitude and direction of the force that the third person should exert to stop the cart, we need to first consider the forces acting on the cart in the x-direction. We have two people pushing the cart with forces F1 and F2, respectively. Let's assume that F1 is exerted to the right and F2 is exerted to the left.
Since the cart is at rest, the net force in the x-direction must be zero. This can be written as:
F_net = F1 - F2 + F3 = 0
Where F3 is the force exerted by the third person.
Since we want to stop the cart, the direction of the force exerted by the third person should be opposite to the net force due to F1 and F2.
Using the fact that F_net = 0, we can rearrange the equation to solve for F3:
F3 = F2 - F1
The magnitude of the force can be found by taking the absolute value of F3, and the direction can be determined based on whether F3 is positive or negative.
(b) To find the weight of the cart, we need to use the information about the cart's acceleration and apply Newton's second law of motion. According to Newton's second law, the net force on an object is equal to the product of its mass (m) and its acceleration (a). In this case, the net force is provided by the force exerted by the third person, which we found in part (a).
So, we can write:
F_net = m * a
Rearranging the equation, we can solve for the mass of the cart:
m = F_net / a
Once we find the mass, we can calculate the weight of the cart using the formula:
Weight = mass * gravitational acceleration
where the gravitational acceleration is approximately 9.8 m/s^2.
To summarize:
(a) The magnitude of the force that the third person should exert to stop the cart is equal to the difference between the magnitudes of the forces exerted by the two people pushing the cart, and the direction of the force should be opposite to the net force due to F1 and F2.
(b) Once we know the magnitude of the force exerted by the third person and the acceleration of the cart, we can calculate the weight of the cart using the formula mass * gravitational acceleration.