A 50 kg box rests on a smooth frictionless table. Connected to the box is a light string passing through a pulley at the end of the table. Suspended on rhe other end of the string is a 20 kg box. Find
a) acceleration of the system,
b) the tension in the string
c) the displacement 15 seconds after starting from rest.
Thank you.
F = 20 * 9.8
m = 50 + 20 = 70
a = F/m = 2.8 m/s^2
force on falling 20 kg mass
= 20 (9.8) - T
= m a = 20(2.8)
so T = 140 Newtons
d = (1/2) a t^2
= (1/2) 2.8 (225)
= 315
are you sure you did not mean 1.5 seconds?
Hi Damon. Thank you. It is written on my book, it's really 15 seconds.
big table :)
The table is three football fields long and three football fields high?
I bet it was 0.15 seconds actually :)
Okay then. Maybe it's a typo. I'll ask my teacher about this tom :) uhmm anyway, how can you get the acceleration of the two boxes and tension in the cord if you just have 53 degrees and 30 degrees?
I do not understand this geometry. Is the big one trying to drop down a 53 deg slope and the little one being dragged up a 30 degree slope or what?
Still physics. It has a figure shown here. Can't show u the picture. But its like, theres a box and another box suspended by a cord on either sides of a pulley creating 30 deg and 50 deg.
All I can do is tell you the method.
call M1 the mass of the one that is on string at 50 degrees from vertical (aI assume from vertical
Then gravity force down slope is
M1 g cos 50
T is up slope
net force down is (M1 g cos 50 -T)
same deal for M2
net force down is (M2 g cos 30 -T) 30
difference in those two forces = net force = (M1+M2)a
moreover F = m a for each of the two masses
To solve this problem, we will use Newton's second law of motion, which states that the sum of the forces acting on an object is equal to its mass multiplied by its acceleration.
First, let's consider the system as a whole. The tension in the string will be the same for both boxes because they are connected by the string. Therefore, we only need to find the acceleration of the system and we can use that to find the tension in the string.
a) To find the acceleration of the system, we need to analyze the forces acting on the boxes. The only external force acting on the system is the weight of the 20 kg box, which is equal to its mass multiplied by the acceleration due to gravity, g.
Weight of 20 kg box = mass × acceleration due to gravity
= 20 kg × 9.8 m/s^2
= 196 N
Since the boxes are connected by the string and there is no friction, the tension in the string will balance the weight of the 20 kg box. Therefore, the tension in the string is also 196 N.
Now, we can apply Newton's second law separately to each box.
For the 50 kg box:
net force = mass × acceleration
Tension in the string - Weight = mass × acceleration
Tension in the string - 50 kg × 9.8 m/s^2 = 50 kg × acceleration
For the 20 kg box:
net force = mass × acceleration
Weight - Tension in the string = mass × acceleration
20 kg × 9.8 m/s^2 - Tension in the string = 20 kg × acceleration
Since the tension in the string is the same for both boxes, we can set up a system of equations to solve for the acceleration:
Tension in the string - 50 kg × 9.8 m/s^2 = 50 kg × acceleration
20 kg × 9.8 m/s^2 - Tension in the string = 20 kg × acceleration
Plugging in the value we found for the tension in the string:
196 N - 50 kg × 9.8 m/s^2 = 50 kg × acceleration
20 kg × 9.8 m/s^2 - 196 N = 20 kg × acceleration
Simplifying these equations, we get:
acceleration = (196 N - 50 kg × 9.8 m/s^2) / 50 kg
acceleration = (20 kg × 9.8 m/s^2 - 196 N) / 20 kg
Now we can calculate the acceleration.
b) The tension in the string is the same as we found earlier, which is 196 N.
c) To find the displacement after 15 seconds, we need to find the average velocity of the system using the formula:
average velocity = initial velocity + (acceleration × time)
Since the system started from rest, the initial velocity is 0 m/s. Therefore, the formula becomes:
average velocity = acceleration × time
Using the value we found for acceleration, we can calculate the average velocity:
average velocity = acceleration × 15 s
Finally, the displacement can be found using the formula:
displacement = average velocity × time
Using the average velocity we found earlier, we can calculate the displacement after 15 seconds.