Imagine a right-angle triangle with angle θ = 40o on the left. The serves as an increasing slope. On the slope is
an object of mass m1= 340 g on an inclined surface. The angle of the inclined surface is θ = 40o with the horizontal. The object m1 is connected to a second object of mass m2 = 338 g on the adjacent horizontal surface.
Now imagine a hand pulling object of mass m1 so that it climbs the slope.
This is the external force of magnitude ІFextІ = 5.5 N, exerted on the object of mass m1. We observe both objects to accelerate. Assuming that the surfaces and the pulley are frictionless, and the pulley and the connecting string are massless, what is the tension in the string connecting the two objects?
http://www.jiskha.com/display.cgi?id=1254845390
I don't understand that working I am sorry. I don't get the bit about the external force because as far as I know gravity shouldn't be part of the external force because someone is pulling on m1 so it slides up the slope =/
i am very confused
i tried solving it that way but i got stuck because i don't know what to do with the external force value :S
To find the tension in the string connecting the two objects, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Let's break down the problem step by step:
1. Calculate the acceleration of the system:
Since both objects are connected by a string and there is no friction, the acceleration of both objects will be the same. Let's assume the acceleration of the system is "a".
2. Determine the net force acting on object m1:
The only external force acting on object m1 is the external force, F_ext, which is exerted by the hand.
F_net1 = F_ext
3. Resolve the net force into horizontal and vertical components:
Since the inclined surface makes an angle of 40 degrees with the horizontal, we need to resolve the forces into horizontal and vertical components. The weight of object m1 can be resolved as follows:
Vertical component: F_w1_vertical = m1 * g * cosθ
Horizontal component: F_w1_horizontal = m1 * g * sinθ
Note: "g" represents the acceleration due to gravity, approximately 9.8 m/s^2.
Since the surfaces and the pulley are frictionless, there are no other forces acting on object m1.
4. Apply Newton's second law to object m1:
F_net1_horizontal = m1 * a
5. Determine the net force acting on object m2:
Since the two objects are connected by a string, the tension in the string will be the force acting on object m2.
F_net2 = Tension
6. Apply Newton's second law to object m2:
F_net2 = m2 * a
7. Equate the forces and solve for Tension:
Setting F_net1_horizontal equal to F_net2:
m1 * g * sinθ = m2 * a
We already have the values of m1, m2, g, and θ. We need to find the value of a.
8. Determine the value of a:
To find the value of acceleration, we can use the relationship between acceleration and net force.
F_net1_horizontal = F_ext
m1 * a = F_ext
Divide both sides by m1 to solve for a:
a = F_ext / m1
Substitute the given values of F_ext and m1 to find the value of acceleration.
9. Calculate the tension T:
Rearrange the equation F_net1_horizontal = F_net2 to solve for Tension:
m1 * g * sinθ = m2 * a
Substitute the calculated value of acceleration, mass values, and θ into the equation to find the tension in the string connecting the two objects.