A cable with 21.2 N of tension pulls straight up on a 1.10 kg block that is initially at rest. What is the block's speed (in m/s) after being lifted 2.42 m assuming that the local acceleration due to gravity is 9.80 m/s2?
We know that,
W = KE + PE ----> *
W = F x d
KE = 1/2 m v^2
PE = mgh
putting all this in *,
(F)(d) = 1/2 m v^2 + mgh
Rearranging,
v = sqrt[2[(F)(d)-(m)(g)(h)]/m]
Plugging in the values we get,
v = sqrt[2[(21.2N)(2.42m)-(1.1kg)(9.8m/s^2)(2.42m)]/1.1kg]
v = 6.77 m/s
Well, if you're looking to lift someone's spirits with this question, I'm here to help! Let's see if I can calculate this using my funny bone.
First, let's address the tension in the cable. It's pulling straight up with 21.2 Newtons of force. That's like trying to hold back your laughter when someone tells a really corny joke!
Now, the block weighs about 1.10 kg. That's not too heavy - it's like a featherweight champion in the world of blocks! And we're lifting it by 2.42 meters. That's quite the elevator ride!
Next, we need to consider the local acceleration due to gravity, which is 9.80 m/s2. It's like a constant force that pulls us all down to earth, reminding us that what goes up must come down!
Now, let's bring it all together. We can use the work-energy theorem to find the velocity of the block after being lifted.
The work done on an object is equal to the change in its kinetic energy. In this case, the work done is equal to the force (21.2 N) times the distance (2.42 m).
So, the work done is 21.2 N * 2.42 m = 51.344 J. That's about as much work as wearing a clown nose all day without it falling off!
Now, we can use the equation for work done: Work = Change in kinetic energy. The change in kinetic energy is equal to 1/2 * mass * velocity^2.
Solving for velocity, we have: velocity = sqrt(2 * Work / mass) = sqrt(2 * 51.344 J / 1.10 kg).
After crunching the numbers, the block's speed comes out to be approximately 8.25 m/s. That's faster than a clown on roller skates!
So, there you have it! The block's speed after being lifted 2.42 m is around 8.25 m/s. Just remember, no need to clown around with the numbers - they can be serious business!
To find the speed of the block after being lifted, we need to consider the work done on the block by the tension in the cable.
The work done on an object is given by the equation:
Work = Force × Distance × Cos(theta)
where:
Force is the applied force (tension in the cable),
Distance is the distance moved in the direction of the force (2.42 m),
and Cos(theta) is the angle between the force and the direction of displacement (in this case, since the cable pulls vertically upward, the angle is 0°, and hence Cos(0°) = 1).
In this case, the work done on the block is equal to the change in its kinetic energy.
So, we can write:
Work = Change in kinetic energy
The change in kinetic energy is given by:
Change in kinetic energy = 1/2 × mass × final velocity^2 - 1/2 × mass × initial velocity^2
Since the block is initially at rest, the initial velocity is 0. Therefore, the equation becomes:
Change in kinetic energy = 1/2 × mass × final velocity^2 - 1/2 × mass × 0^2
Change in kinetic energy = 1/2 × mass × final velocity^2
We can equate this change in kinetic energy to the work done:
1/2 × mass × final velocity^2 = Force × Distance × Cos(theta)
Substituting the given values:
1/2 × 1.10 kg × final velocity^2 = 21.2 N × 2.42 m × 1
Simplifying the equation:
Final velocity^2 = (21.2 N × 2.42 m) / (1/2 × 1.10 kg)
Final velocity^2 = 51.424 m^2/s^2
Taking the square root of both sides:
Final velocity = √(51.424 m^2/s^2)
Final velocity ≈ 7.17 m/s
Therefore, the block's speed after being lifted 2.42 m is approximately 7.17 m/s.
To find the block's speed after being lifted, we can use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy.
The work done is given by the equation:
Work = Force * Distance * cos(θ)
In this case, the force is the tension in the cable (21.2 N), the distance is the height the block is lifted (2.42 m), and θ is the angle between the force and the direction of motion (in this case, cos(θ) = 1 since the force and motion are in the same direction).
So, the work done on the block is:
Work = 21.2 N * 2.42 m * 1 = 51.3044 J
Now, we can use the work-energy theorem to find the final kinetic energy of the block:
Work = ΔKE (change in kinetic energy)
51.3044 J = ΔKE
We can assume that the initial kinetic energy is zero since the block is initially at rest.
So, the change in kinetic energy is:
ΔKE = Final KE - Initial KE
= Final KE - 0
= Final KE
Therefore, the change in kinetic energy is equal to the final kinetic energy.
Now, we can equate the work done to the change in kinetic energy to find the final kinetic energy:
51.3044 J = Final KE
Finally, we can use the formula for kinetic energy to find the final velocity of the block:
KE = 1/2 * m * v^2
Rearranging the equation:
Final KE = 1/2 * m * v^2
Substituting the values:
51.3044 J = 1/2 * 1.10 kg * v^2
Simplifying:
v^2 = 2 * (51.3044 J) / 1.10 kg
v^2 = 93.3712 m^2/s^2
Taking the square root of both sides:
v = √(93.3712 m^2/s^2)
v ≈ 9.665 m/s
Therefore, the block's speed after being lifted 2.42 m is approximately 9.665 m/s.
Net force= totalmass*(g+a)
solve for a.
then speed^2=2*acceleration*distance