A 2.3 kg steel block is at rest on a steel table. A horizontal string pulls on the block. The coefficient of static friction for steel on steel is 0.80 (page 163) while the coefficient of kinetic friction is 0.60 while the acceleration due to gravity is 9.80 m/s2. If the tension in the string is 20.0 N, what is the block's speed (in m/s) after moving 1.7 m?
tension-friction= mass*acceleration
20.0-.6*2.3*9.8= 2.3*a
solve for acceleration, a.
vf^2=2ad solve for Vf
To find the block's speed after moving 1.7 m, we first need to determine whether the block will move or not. This can be done by comparing the applied force (tension in the string) with the maximum static friction force.
The maximum static friction force can be calculated using the equation:
f_static_max = μ_static * N
where μ_static is the coefficient of static friction and N is the normal force acting on the block.
The normal force can be determined using the equation:
N = m * g
where m is the mass of the block and g is the acceleration due to gravity.
N = 2.3 kg * 9.8 m/s^2
N = 22.54 N
Now, we can calculate the maximum static friction force:
f_static_max = 0.8 * 22.54 N
f_static_max = 18.03 N
Since the tension in the string (applied force) is 20.0 N, which is greater than the maximum static friction force, the block will move.
Next, we need to calculate the net force acting on the block. This can be done by subtracting the kinetic friction force from the applied force:
f_net = applied force - f_kinetic
The kinetic friction force can be calculated using the equation:
f_kinetic = μ_kinetic * N
where μ_kinetic is the coefficient of kinetic friction.
f_kinetic = 0.6 * 22.54 N
f_kinetic = 13.524 N
Now, we can calculate the net force:
f_net = 20.0 N - 13.524 N
f_net = 6.476 N
Now, we can use Newton's second law of motion to find the acceleration of the block:
f_net = m * a
a = f_net / m
a = 6.476 N / 2.3 kg
a ≈ 2.82 m/s^2
Finally, we can use the kinematic equation to find the block's speed after moving 1.7 m:
v^2 = u^2 + 2a * d
where v is the final velocity, u is the initial velocity (which is 0 since the block was at rest), a is the acceleration, and d is the distance traveled.
Plugging in the values:
v^2 = 0^2 + 2 * 2.82 m/s^2 * 1.7 m
v^2 = 9.636 m^2/s^2
v ≈ √9.636 ≈ 3.11 m/s
Therefore, the block's speed after moving 1.7 m is approximately 3.11 m/s.
To find the block's speed after moving 1.7 m, we need to determine if the block remains at rest or if it starts moving due to the applied tension. The maximum force of static friction can be calculated using the formula:
F_static_max = coefficient of static friction * normal force
The normal force acting on the block is equal to the weight of the block, which can be calculated as:
weight = mass * acceleration due to gravity
Once we know the maximum force of static friction, we can compare it to the tension in the string to determine if the block remains at rest or if it starts moving. If the tension is greater than the force of static friction, the block will start moving and the force of kinetic friction will take over.
The force of kinetic friction can be calculated using the formula:
F_kinetic = coefficient of kinetic friction * normal force
If the block starts moving, the work done by the tension force will be equal to the work done against the force of kinetic friction. The work done can be calculated using the formula:
work = force * distance
Finally, the block's speed can be found using the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy:
work = change in kinetic energy
0.5 * mass * speed^2 = work
By rearranging the formula, we can find the speed:
speed = sqrt(2 * work / mass)
Now, let's go ahead and calculate the block's speed:
1. Calculate the maximum force of static friction:
F_static_max = 0.80 * weight
2. Calculate the weight of the block:
weight = mass * acceleration due to gravity
3. Determine if the block starts moving or remains at rest:
Compare the tension in the string to the maximum force of static friction.
If tension > F_static_max, go to step 4.
If tension ≤ F_static_max, the block remains at rest and the speed is 0 m/s.
4. Calculate the force of kinetic friction:
F_kinetic = 0.60 * weight
5. Calculate the work done by the tension force:
work = tension * distance
6. Calculate the block's speed:
speed = sqrt(2 * work / mass)
By following these steps, you will be able to determine the block's speed after moving 1.7 m.