You push against a steamer trunk at an angle of 33° with the horizontal . The trunk is on a flat floor and the coefficient of static friction between the trunk and floor is 0.55. The mass of the trunk is 43 kg. What is the minimum magnitude of force that will allow you to move the trunk?
M*g = 45 * 9.8 = 441 N. = Wt. of trunk.
Fn = 441 + F*sin33.
Fs = u*Fn = 0.55(441+F*sin33) = 242.6 +
0.3F.
(F-Fs) = M*a.
(F-(242.6+0.3F) = M*0.
F - 242.6 - 0.3 = 0
0.7F = 242.6.
F = 347 N.
To determine the minimum magnitude of force required to move the trunk, we need to consider the forces acting on the trunk. In this case, there are two main forces to consider: the force of gravity acting vertically downward and the static friction that opposes the motion horizontally.
First, we need to find the force due to gravity acting on the trunk. The force due to gravity can be calculated using the formula:
Force due to gravity (Fg) = mass (m) * acceleration due to gravity (g)
Given that the mass of the trunk (m) is 43 kg and the acceleration due to gravity (g) is approximately 9.8 m/s^2:
Fg = 43 kg * 9.8 m/s^2
≈ 421.4 N
Next, we need to determine the maximum static friction force that can be exerted on the trunk. The maximum static friction force can be calculated using the formula:
Maximum static friction force (Fs_max) = coefficient of static friction (μ) * normal force (Fn)
The normal force (Fn) can be calculated using the formula:
Normal force (Fn) = mass (m) * acceleration due to gravity (g) * cos(angle)
where the angle is the angle between the trunk and the horizontal plane. In this case, the angle is given as 33°.
Fn = 43 kg * 9.8 m/s^2 * cos(33°)
≈ 360.67 N
Now, we can calculate the maximum static friction force:
Fs_max = 0.55 * 360.67 N
≈ 198.37 N
Since the static friction force opposes the applied force, the minimum magnitude of force required to move the trunk (F) is equal to the maximum static friction force:
F = Fs_max
≈ 198.37 N
Therefore, the minimum magnitude of force required to move the trunk is approximately 198.37 N.
To determine the minimum magnitude of force required to move the trunk, we need to consider the forces acting on the trunk and calculate the force of static friction.
The forces acting on the trunk are its weight (mg) and the normal force (N) exerted by the floor. The weight of the trunk is given by the mass (m) multiplied by the acceleration due to gravity (g), which is approximately 9.8 m/s². Therefore, the weight of the trunk is:
Weight (W) = mg = 43 kg * 9.8 m/s² = 421.4 N
The normal force (N) is equal to the weight of the trunk since the trunk is on a flat floor without any vertical acceleration. So N = 421.4 N.
The force of static friction (Fstatic) opposes the horizontal force we apply and prevents the trunk from moving. The formula for the force of static friction is:
Fstatic = μs * N
Here, μs represents the coefficient of static friction, and N is the normal force.
Plugging in the values, we get:
Fstatic = 0.55 * 421.4 N ≈ 231.77 N
Therefore, the minimum magnitude of force required to move the trunk is approximately 231.77 Newtons.