160 m/s because you start off with 10 and go up by 50*3 which is 150 then add that with the begging speed to achieve 160m/s.
Answer:
The coefficient of friction and acceleration are 0.37 and 2.2 m/s²
Explanation:
Suppose we find the coefficient of friction and the acceleration of the 100 kg block during the time that the 60 kg block remains in contact.
Given that,
Mass of block = 60 kg
Acceleration = 2.0 m/s²
Mass = 100 kg
Horizontal force = 340 N
Let the frictional force be f.
We need to calculate the frictional force
Using balance equation
Put the value into the formula
We need to calculate the coefficient of friction
Using formula of friction force
We need to calculate the acceleration of the 100 kg block
Using formula of newton's law
Hence, The coefficient of friction and acceleration are 0.37 and 2.2 m/s²
Answer:
The tension in the rope is 41.38 N.
Explanation:
Given that,
Mass of bucket of water = 14.0 kg
Diameter of cylinder = 0.260 m
Mass of cylinder = 12.1 kg
Distance = 10.7 m
Suppose we need to find that,
What is the tension in the rope while the bucket is falling
We need to calculate the acceleration
Using relation of torque
Where, I = moment of inertia
= angular acceleration
...(I)
Here, F = tension
The force is
...(II)
Where, F = tension
a = acceleration
From equation (I) and (II)
Put the value into the formula
We need to calculate the tension in the rope
Using equation (I)
Put the value into the formula
Hence, The tension in the rope is 41.38 N.
Answer:
39.81 N
Explanation:
I attached an image of the free body diagrams I drew of crate #1 and #2.
Using these diagram, we can set up a system of equations for the sum of forces in the x and y direction.
∑Fₓ = maₓ
∑Fᵧ = maᵧ
Let's start with the free body diagram for crate #2. Let's set the positive direction on top and the negative direction on the bottom. We can see that the forces acting on crate #2 are in the y-direction, so let's use Newton's 2nd Law to write this equation:
- ∑Fᵧ = maᵧ
- T₁ - m₂g = m₂aᵧ
Note that the tension and acceleration are constant throughout the system since the string has a negligible mass. Therefore, we don't really need to write the subscripts under T and a, but I am doing so just so there is no confusion.
Let's solve for T in the equation...
- T₁ = m₂aᵧ + m₂g
- T₁ = m₂(a + g)
We'll come back to this equation later. Now let's go to the free body diagram for crate #1.
We want to solve for the forces in the x-direction now. Let's set the leftwards direction to be positive and the rightwards direction to be negative.
The normal force is equal to the x-component of the force of gravity.
- (F_n · μ_k) - m₁g sinΘ = m₁aₓ
- (F_g cosΘ · μ_k) - m₁g sinΘ = m₁aₓ
- [m₁g cos(30) · 0.28] - [m₁g sin(30)] = m₁aₓ
- [(6)(9.8)cos(30) · 0.28] - [(6)(9.8)sin(30)] = (6)aₓ
- [2.539595871] - [-58.0962595] = 6aₓ
- 60.63585537 = 6aₓ
- aₓ = 10.1059759 m/s²
Now let's go back to this equation:
We have 3 known variables and we can solve for the tension force.
- T = 2(10.1059759 + 9.8)
- T = 2(19.9059759)
- T = 39.8119518 N
The tension force is the same throughout the string, therefore, the tension in the string connecting M2 and M3 is 39.81 N.