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1. Based on the mc free-body diagram, type an expression for the horizontal acceleration of the cart only in terms of T , mh , mc , μk , and g .

2.Based on the mh free-body diagram, type an expression for the vertical acceleration of the hanging mass.

3. As shown in the first figure, the horizontal acceleration of the cart to the right must be equal to the downward vertical acceleration of the hanging mass if the string does not stretch. Given that both the cart and the hanging mass have the same acceleration, eliminate the tension force ( T ) from your answers to Q1 and Q2 to find an expression for the acceleration only in terms of mh , mc , μk , and g .

1 Based on the mc freebody diagram type an expression for the horizontal acceleration of the cart only in terms of T mh mc μk and g 2Based on the mh freebody di class=

Respuesta :

onyebuchinnaji

(a) The expression for the horizontal acceleration of the cart is

a = (T - μN)/Mc.

(b) The expression for the vertical acceleration of the hanging mass is

a = (T - Mhg)/Mh.

(c) The expression for the acceleration of both cart and the hanging mass is a = (Mhg - μN) / (Mc - Mh).

Horizontal acceleration of the cart

The horizontal acceleration of the cart is calculated as follows;

The horizontal acceleration of the cart is determined from the net horizontal force acting on the system.

T - μN = Mca

where;

  • Mc is mass of the cart
  • a is the acceleration of the cart

a = (T - μN)/Mc

Vertical acceleration of the hanging mass

T - Mhg = Mha

where;

  • Mh is the mass of the hanging mass

a = (T - Mhg)/Mh

Acceleration of both objects

If the acceleration of the cart and the hanging mass are equal, our final equation becomes;

From first equation;

a = (T - μN)/Mc

Mca = T - μN

Mca + μN = T

From second equation;

a = (T - Mhg)/Mh

Mha = T - Mhg

Mha + Mhg = T

Solve the two equation together;

Mca + μN = Mha + Mhg

Mca - Mha = Mhg - μN

a(Mc - Mh) = Mhg - μN

a = (Mhg - μN) / (Mc - Mh)

Thus, the expression for the acceleration of both cart and the hanging mass is a = (Mhg - μN) / (Mc - Mh).

Learn more about horizontal acceleration here: https://brainly.com/question/14268089

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