16)You are pushing a 55N lawnmower across the yard. Its handle makes a 55 degree angle with the ground. What force are you exerting on the handle?
A)1 N
B)67.1 N
C)95.89 N
D)3025 N
I got C
17)Two men pull a 31 kg box with forces 9.7 N and 7.6 N in both directions. Find the resultant acceleration of the box and the direction in which the box moves.
A)2.1 m/s^2 to the left
B)2.1 m/s^2 to the right
C)6.8 x 10^-2 m/s^2 to the left
D)6.8 x 10^-2 m/s^2 to the right
I got A
16) Insufficient data for any answer. One needs to know the frictional and lawn-cutting resistance force, and whather the lawnmower is accelerating. You can push with any force you like on a 55N (weight)lawnmower. It's weight is supported by the vertical ground force on the wheels, not you pushing the handle.
Whoever assigned that problem should not be teaching physics
17) Wrong. Net force = 2.1 N. Divide than by mass for the acceleration. It will be in the direction of the larger force
To solve these problems, you need to apply Newton's laws of motion and resolve forces into their components.
16) In this question, you are pushing a lawnmower with a given force and angle. To find the force you are exerting on the handle, you need to resolve the given force vector into its vertical and horizontal components.
The vertical component of the force is given by:
F_vertical = F * sin(angle)
F_vertical = 55 N * sin(55°)
F_vertical ≈ 46.08 N (rounded to two decimal places)
The horizontal component of the force is given by:
F_horizontal = F * cos(angle)
F_horizontal = 55 N * cos(55°)
F_horizontal ≈ 33.61 N (rounded to two decimal places)
Therefore, the force you are exerting on the handle is the horizontal component, which is approximately 33.61 N. Thus, the correct answer is B) 33.61 N.
17) Here, you have two forces acting in opposite directions. To find the resultant acceleration and direction of the box, you need to calculate the net force acting on it.
Combine the forces acting on the box:
Net force = 9.7 N - 7.6 N
Net force = 2.1 N (Towards the right)
Next, use Newton's second law of motion:
F = m * a
2.1 N = 31 kg * a
Solve for acceleration (a):
a = 2.1 N / 31 kg
a ≈ 0.068 m/s^2 (rounded to two decimal places)
The positive value for acceleration indicates that the box moves to the right. Therefore, the correct answer is B) 2.1 m/s^2 to the right.