Starting from rest Maria pulls horizontally on her new wagon for 1.1 seconds. She exerts a constant force of 89N against a frictional force of 43N. The wagon's final velocity is 3.2m/s. If she is on a level ground, how much does the wagon weigh?
Fnet= m a= m *3.2/1.1
89-43=m * 3.2/1.1 solve for m
weight= mg
Use the fact that impulse
= (net force)*(time) = (momentum change)
The momentum given to the wagon is
(89 - 43)* 1.1 = 50.5 kg m/s
Divide that by the final velocity to get the mass in kg.
To calculate the weight of the wagon, we need to understand the forces acting on it. In this scenario, there are two main forces: the force Maria exerts (89N) and the frictional force opposing the motion (43N). The net force acting on the wagon is the difference between these two forces:
Net force = Force applied by Maria - Frictional force
The net force is also related to the acceleration of the wagon using Newton's second law of motion (F = ma), where F is force and a is acceleration. In this case, we can assume that the wagon starts from rest and achieves a final velocity of 3.2 m/s in 1.1 seconds.
The equation to relate force, mass, and acceleration is:
Net force = (mass of the wagon) * (acceleration of the wagon)
Given that the net force is the force applied by Maria minus the frictional force, and the acceleration is the change in velocity divided by the time taken, the equation becomes:
(Force applied by Maria - Frictional force) = (mass of the wagon) * (final velocity - initial velocity) / time
Since the wagon starts from rest, the equation simplifies to:
(Force applied by Maria - Frictional force) = (mass of the wagon) * final velocity / time
Now, we need to rearrange the equation to find the mass of the wagon:
mass of the wagon = (Force applied by Maria - Frictional force) * time / final velocity
Substituting the given values:
mass of the wagon = (89N - 43N) * 1.1s / 3.2m/s
mass of the wagon = 46N * 1.1s / 3.2m/s
Finally, we can calculate the weight of the wagon using the formula:
weight = mass of the wagon * acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.8 m/s^2. Substituting the mass value:
weight = (46N * 1.1s / 3.2m/s) * 9.8 m/s^2
weight = 16.72 kg * 9.8 m/s^2
weight ≈ 164 N
Therefore, the weight of the wagon is approximately 164 Newtons.