• Moe, lary and curly push on a 752Kg boat that floats
next to dock. They each exert an 80.5N force parallel to
the dock
• (a)What is the acceleration of the boat if they all push in
same direction?Give both direction and magnitude
• (b) What are the magnitude and direction of the boats
acceleration if larry and curly push in the opposite
direction to Moe,s push?
(a) Well, first things first, we gotta find the net force on the boat. Since Moe, Larry, and Curly are all pushing in the same direction, we just add up their individual forces.
So, the net force is 80.5N + 80.5N + 80.5N = 241.5N.
Now, we can use Newton's second law, F = ma, to find the acceleration. Rearranging the equation, we have a = F/m.
Given that the mass of the boat is 752kg, we can plug in the numbers: a = 241.5N / 752kg ≈ 0.321m/s².
So, the acceleration of the boat, with both magnitude and direction, is approximately 0.321m/s² in the same direction as the pushing.
(b) In this scenario, Moe is pushing in one direction, while Larry and Curly are pushing in the opposite direction. This means that their forces will subtract from each other.
The net force would then be 80.5N - 80.5N - 80.5N = -80.5N (negative sign indicating opposite direction).
Using Newton's second law again, we have a = F/m. Plugging in the numbers, a = -80.5N / 752kg ≈ -0.107m/s².
So, the magnitude of the boat's acceleration is approximately 0.107m/s², while the direction is opposite to Moe's push.
(a) To find the acceleration of the boat when Moe, Larry, and Curly push in the same direction, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass.
Given:
- Mass of the boat (m) = 752 kg
- Force exerted by each person (F) = 80.5 N
We can calculate the net force exerted on the boat when they all push in the same direction:
Net force (F_net) = F + F + F
= 80.5 N + 80.5 N + 80.5 N
= 241.5 N
Next, we can calculate the boat's acceleration:
Acceleration (a) = F_net / m
= 241.5 N / 752 kg
≈ 0.321 m/s²
Therefore, the magnitude of the boat's acceleration when they all push in the same direction is approximately 0.321 m/s², parallel to the dock.
(b) When Larry and Curly push in the opposite direction to Moe's push, we need to consider the direction and magnitude of the forces.
Force exerted by Moe (F_moe) = 80.5 N (towards the right)
Force exerted by Larry and Curly (F_lc) = 80.5 N (towards the left)
The net force (F_net) is the difference between these two forces:
F_net = F_moe - F_lc
= 80.5 N - 80.5 N
= 0 N
Since the net force is zero, the boat will not experience any acceleration. It will remain stationary.
Therefore, the magnitude of the boat's acceleration when Larry and Curly push in the opposite direction to Moe's push is zero, and the direction is also zero (no acceleration).
To find the acceleration of the boat, we can use Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
(a) When Moe, Larry, and Curly all push in the same direction, we need to sum up their individual forces to find the net force on the boat. Since they are pushing in the same direction, we can simply add their forces:
Total force = Moe's force + Larry's force + Curly's force
Given that each of them exerts an 80.5N force, we can substitute the values:
Total force = 80.5N + 80.5N + 80.5N = 241.5N
Now, we can calculate the acceleration of the boat using Newton's Second Law:
Net force = mass of the boat × acceleration
Rearranging the equation to solve for acceleration:
Acceleration = Net force / mass of the boat
Plugging in the values, we get:
Acceleration = 241.5N / 752kg ≈ 0.321m/s²
So, the magnitude of the boat's acceleration is approximately 0.321m/s², and since they are pushing in the same direction, the boat accelerates in that direction as well.
(b) When Larry and Curly push in the opposite direction to Moe's push, we need to subtract their forces from Moe's force to find the net force on the boat:
Total force = Moe's force - Larry's force - Curly's force
Substituting the values:
Total force = 80.5N - 80.5N - 80.5N = -80.5N
Here, we have a negative sign indicating that the net force is in the opposite direction to Moe's push.
Now, we can calculate the acceleration using the formula:
Acceleration = Net force / mass of the boat
Plugging in the values, we get:
Acceleration = -80.5N / 752kg ≈ -0.107m/s²
So, the magnitude of the boat's acceleration is approximately 0.107m/s², and since the net force is in the opposite direction to Moe's push, the boat accelerates in the opposite direction as well.
when they push in the same direction, just add up all the forces to get F
Otherwise, subtract those forces pushing backwards.
Now recall that F = ma
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