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) To find the force you are exerting on the handle, you can use the magnitude of the force equation:
force = magnitude of force × sine of angle
In this case, the magnitude of force is 55 N and the angle is 55°:
force = 55 N × sin(55°)
Calculating this, we get:
force ≈ 55 N × 0.819 ≈ 45.05 N
So, the correct answer is option C) 45.05 N.
17) To find the resultant acceleration of the box, you can use Newton's second law of motion:
resultant force = mass × acceleration
Given forces F1 = 9.7 N and F2 = 7.6 N acting in opposite directions, the resultant force can be calculated as the difference between the two forces:
resultant force = F1 - F2
resultant force = 9.7 N - 7.6 N
resultant force = 2.1 N to the left
To find the resultant acceleration, we can rearrange the equation:
acceleration = resultant force / mass
Given the mass of the box is 31 kg:
acceleration = 2.1 N / 31 kg
acceleration ≈ 0.0677 m/s^2
Therefore, the box moves with an acceleration of approximately 0.0677 m/s^2 to the left. So, the correct answer is option C) 0.0677 m/s^2 to the left.
To find the force exerted on the handle in question 16, you can use trigonometry. The force you exert on the handle can be determined by finding the component of the force perpendicular to the ground.
To do this, you can use the equation:
Force perpendicular = Force applied * sin(angle)
In this case, the Force applied is 55N and the angle is 55 degrees. So, the force exerted on the handle would be:
Force exerted on handle = 55N * sin(55°)
Using a scientific calculator, you can calculate the sine of 55 degrees and then multiply it by 55N.
The answer would be:
Force exerted on handle ≈ 47.24 N
So, the correct answer would be B) 67.1 N.
Moving on to question 17, to find the resultant acceleration of the box, you need to consider the forces applied by the two men. Since the forces are in opposite directions, you need to subtract one force from the other to find the resultant force.
Resultant force = 9.7 N - 7.6 N
Resultant force = 2.1 N
Now, you can use Newton's second law (F = m * a) to find the acceleration of the box. The mass of the box is given as 31 kg. Plugging in the values, you get:
2.1 N = 31 kg * acceleration
Solve for acceleration:
acceleration ≈ 2.1 N / 31 kg
acceleration ≈ 0.068 m/s²
The acceleration is to the left, which means the box moves to the left. Therefore, the correct answer is A) 2.1 m/s² to the left.